Method of Surface of Section Applied to a Possible Capture Origin of Jupiter's Satellites

Extract

The capture of satellites is considered to be a slow process, in which particles approaching the planet lose their energy gradually and fall down into the stable orbits around it. Therefore, in order to investigate the capture problem, it seems to be necessary to clarify the behaviors of orbits near the planet. Recently Hayashi et al. (1977) and Heppenheimer and Porco (1977) found that in the restricted three body problem, particles incident through Lagrange points L₁ and L₂ revolve always directly around Jupiter as long as the potential windows at L₁ and L₂ are small. This suggests the impossibility of the capture of retrograde satellites when the potential windows are small.